We state a problem on uniformly stressed reinforcement for three-layer pure membrane shells under elastic and non-elastic deformation of material of phases. We perform qualitative analysis of systems of governing equations for shells of various Gaussian curvatures. We obtain analytical solutions for the problem on uniformly stressed reinforcement of shells of revolution under the conditions of uniform deformation; we consider shells of constant and varying thickness with various quantities of families of fibers. Considering some particular examples, we arrive at the conclusion that the employment of non-elastic structures allows us to reduce the quantity of fibers by several times or to increase the bearing ability of structures as compared to elastic cases.